Question: A club had collected an amount of money to split among the top three finishers of their annual science fair. The first place finisher will receive one-half of the money. The second place finisher will receive one-third of the money. The third place finisher will receive $200. How much money will the first place finisher receive?
Explanation: We set the total amount of money to be $x$. The first place finisher gets $\frac{x}{2}$ dollars. The second place finisher gets $\frac{x}{3}$ dollars. Since the third place finisher gets the rest, he gets $x-\frac{x}{2}-\frac{x}{3} = \frac{x}{6}$ dollars. Since he got $200, $\frac{x}{6}=200$. Solving, we get $x=1200$ dollars. Since the first place finisher gets half, he gets $\boxed{\$600}.$